Graphs with Few Eigenvalues

Brouwer, Andries E.; Haemers, Willem H.

doi:10.1007/978-1-4614-1939-6_15

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Fiedlers's Lemma1

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2021

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Cited by 2 publications

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“…Lemma 3.2. [14] If G is a kregular graph of order n, and k, λ 2 , ..., λ n are the adjacency eigenvalues of G, then…”

Section: Fiedlers's Lemmamentioning

confidence: 99%

Seidel Laplacian and Seidel Signless Laplacian Spectrum of the Zero-divisor Graph on the Ring of Integers Modulo <img src=image/13424080_01.gif>

Magi¹,

Jose²,

Kishore³

2021

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“…Lemma 3.2. [14] If G is a kregular graph of order n, and k, λ 2 , ..., λ n are the adjacency eigenvalues of G, then…”

Section: Fiedlers's Lemmamentioning

confidence: 99%

Seidel Laplacian and Seidel Signless Laplacian Spectrum of the Zero-divisor Graph on the Ring of Integers Modulo <img src=image/13424080_01.gif>

Magi¹,

Jose²,

Kishore³

2021

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Some Families of Orthogonal Polynomials of a Discrete Variable and their Applications to Graphs and Codes

Cámara¹,

Fàbrega²,

Fiol³

et al. 2009

Electron. J. Combin.

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We present some related families of orthogonal polynomials of a discrete variable and survey some of their applications in the study of (distance-regular) graphs and (completely regular) codes. One of the main peculiarities of such orthogonal systems is their non-standard normalization condition, requiring that the square norm of each polynomial must equal its value at a given point of the mesh. For instance, when they are defined from the spectrum of a graph, one of these families is the system of the predistance polynomials which, in the case of distance-regular graphs, turns out to be the sequence of distance polynomials. The applications range from (quasi-spectral) characterizations of distance-regular graphs, walk-regular graphs, local distance-regularity and completely regular codes, to some results on representation theory.

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Graphs with Few Eigenvalues

Cited by 2 publications

References 42 publications

Seidel Laplacian and Seidel Signless Laplacian Spectrum of the Zero-divisor Graph on the Ring of Integers Modulo <img src=image/13424080_01.gif>

Seidel Laplacian and Seidel Signless Laplacian Spectrum of the Zero-divisor Graph on the Ring of Integers Modulo <img src=image/13424080_01.gif>

Some Families of Orthogonal Polynomials of a Discrete Variable and their Applications to Graphs and Codes

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